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WAEC Mathematics 2015 Paper

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Question : 19

Total: 45

In the diagram, O is the centre,

\overline{RT}

is a diameter, < PQT = 33

^{\circ}

^{\circ}

. Using the diagram, find the size of angle PRS.

76^o
71^o
38^o
33^o

Solution:

Concept:

Use the angle in the same segment theorem and the central angle theorem to relate the given angles to the required angle.

Explanation:

The central angle

\angle TOS = 76^{\circ}

subtends arc

TS

.

The inscribed angle

\angle TRS

also subtends the same arc

TS

.

Therefore,

\angle TRS = \frac{1}{2} \times 76^{\circ} = 38^{\circ}

.

Also,

\angle PQT = 33^{\circ}

and

\angle PRT

subtend the same chord

PT

.

Hence,

\angle PRT = \angle PQT = 33^{\circ}

.

From the diagram,

\angle PRS = \angle PRT + \angle TRS

.

So,

\angle PRS = 33^{\circ} + 38^{\circ} = 71^{\circ}

.

Answer:

B.

71^{\circ}

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